How do I make these PBR roof tiles not flat?
There are 2 different things:

For your normal setup, you need to switch the Image Texture to Non-Color as Christopher says, and the Normal Map to the default Tangent Space (I don't know what's Object Space though):



For your Displacement node. Again switch to Non-Color. Also, you've plugged this node into the Displacement socket of the Output, and you've chosen Surface &gt; Displacement &gt; Displacement &amp; Bump in the material Settings, which means that you want the bump effect but you also want a real displacement effect. The displacement itself acts on real geometry, it can only affect an object that is subidivided enough, otherwise nothing happens. Your roof is just made of one face, so it can't be displaced for real. Therefore for the moment only the bump effect happens (which cumulates with the normal effect, which is ok if this is what you want but it may be redundant. And it will also be redundant with the real displacement):


As you can see here is what it gives if I subdivise enough a plane and give it your setup (I had to decrease the Displacement strength though), not sure the height map is good though, giving the result: